Asymptotic Solutions to a Class of Singular Perturbation Burning Models

SHI Juan-rong; MO Jia-qi

doi:10.21656/1000-0887.360293

Volume 37 Issue 7

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SHI Juan-rong, MO Jia-qi. Asymptotic Solutions to a Class of Singular Perturbation Burning Models[J]. Applied Mathematics and Mechanics, 2016, 37(7): 691-698. doi: 10.21656/1000-0887.360293

Citation:

SHI Juan-rong, MO Jia-qi. Asymptotic Solutions to a Class of Singular Perturbation Burning Models[J]. Applied Mathematics and Mechanics, 2016, 37(7): 691-698. doi: 10.21656/1000-0887.360293

Citation:

SHI Juan-rong, MO Jia-qi. Asymptotic Solutions to a Class of Singular Perturbation Burning Models[J]. Applied Mathematics and Mechanics, 2016, 37(7): 691-698. doi: 10.21656/1000-0887.360293

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Asymptotic Solutions to a Class of Singular Perturbation Burning Models

doi: 10.21656/1000-0887.360293

SHI Juan-rong^1,2,
MO Jia-qi³

¹Anhui Technical College of Mechanical and Electrical Engineering, Wuhu, Anhui 241002, P.R.China;²Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, P.R.China;³School of Mathematics & Computer Science, Anhui Normal University, Wuhu, Anhui 241003, P.R.China

Funds: The National Natural Science Foundation of China(41275062;11202106)

Received Date: 2015-10-27
Rev Recd Date: 2015-11-27
Publish Date: 2016-07-15

Abstract

Abstract

A class of nonlinear singularly perturbed burning models with two parameters were discussed. Firstly, the outer solution to the burning model was constructed with the perturbation method. Secondly, through the introduction of a stretched variable, the initial layer correction term of the solution to the burning model was constructed. Then the multi-scale method and the composite expansion method were used to build the boundary layer correction term of the model solution and find the asymptotic solution to the original initial boundary value problem. Finally, the uniform validity of the obtained asymptotic solution was proved according to the theory of differential inequalities. The proposed solving method for this class of nonlinear singularly perturbed burning models is convenient and practicable.
- burning model,
- asymptotic solution,
- singular perturbation

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References(19)

References

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